Question Two [25]

a. The following quadratic production equation was obtained on maize production in North West province of South Africa . Specifically, Q is the output and X₁ and X₂ are the variable inputs.

Calculate the optimum quantities of X₁ and X₂ that will be required for profit maximization if X₁ is sold for R20 per unit and X₂ is sold for R50 per unit and only R5000 is available for production. [13]

b. Given that , derive the output supply function [12]

Question Three [25]

a. Clearly explain how share tenancy can affect efficiency of food production in South Africa. How do you think that the government's land reform programme can address this problem? [15]

b. Find the degree to which the following functions are homogenous:

i. z=8x+9y ii. z = x²+xy+y² iii. z = x^0.3y ^0.4 iv. z = 2x/y [10]